Computation of Periodic Instability of Stratified Fluid Using Continuous Vortex Sheet Dynamics

Proc. 1997 ASME Fluid Engng. Div. Summer Meeting  (Vancouver, Canada, 6/97), paper No. FEDSM97-3502, 12pps.

Zhimin Hu                                             and             Stephan T. Grilli                        

Postdoctoral Res. Associate                                  Associate Professor                                           
Department of Ocean Engng.                                           
niversity of Rhode Island                                    
Narragansett, RI 02882, USA                            

Abstract :  

A new model is proposed to compute the time evolution of the interface between two inviscid fluids moving with uniform velocity, subjected to instabilities of the Kelvin-Helmholtz (KH) type. In this model, the interface is represented by a Continuous Vortex Sheet (CVS) which both preserves the full nonlinearity of interfacial boundary conditions and provides a higher-order representation of the geometry and field variables than in previously proposed models. Time updating of CVS's geometry and circulation is calculated as a function of gravity, interfacial surface tension, and fluid density difference. An intrinsic variable expansion technique is introduced to deal with the hyper-singularity occurring in the Biot-Savart integrals describing CVS's velocity. The model is applied to predict the nonlinear growth of periodic KH instabilities in a two fluid stratified system. Results demonstrate that the CVS representation provides both higher numerical accuracy and stability and gives a more accurate physical picture of the disturbance evolution than less accurate methods, like point vortex models, used in earlier analyses.

Keywords :

Continuous vortex sheet, stratified fluid instability, KH instability

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